Excited [70,ℓ+][{\bf 70},\ell^+] baryon resonances in large NcN_c QCD

We summarize results obtained in the $1/N_c$ expansion method for the masses of baryon resonances belonging to the $[{\bf 70},\ell^+]$ multiplet. They represent an extension of our previous studies from two to three flavors. A better approach to mixed symmetric states of any angular momentum and parity is also outlined.Comment: 4 pages, 1 figure, uses espcrc2.sty (included), based on a talk given by N. Matagne at the 13th International QCD Conference, QCD06, Montpellier, France, 3-7th July 200

Group theoretical study of nonstrange and strange mixed symmetric baryon states [Nc−1,1][N_c-1,1] in the 1/Nc1/N_c expansion

Using group theory arguments we extend and complete our previous work by deriving all SU(6) exact wave functions associated to the spectrum of mixed symmetric baryon states $[N_c-1,1]$ in the $1/N_c$ expansion. The extension to SU(6) enables us to study the mass spectra of both strange and nonstrange baryons, while previous work was restricted to nonstrange baryons described by SU(4). The wave functions are specially written in a form to allow a comparison with the approximate, customarily used wave functions, where the system is separated into a ground state core and an excited quark. We show that the matrix elements of the flavor operator calculated with the exact wave functions acquire the same asymptotic form at large $N_c$, irrespective of the spin-flavor multiplet contained in $[N_c-1,1]$, while with the approximate wave function one cannot obtain a similar behaviour. The isoscalar factors of the permutation group of $N_c$ particles derived here can be used in any problem where a given fermion system is described by the partition $[N_c-1,1]$, and one fermion has to be separated from the rest.Comment: 19 pages, 7 tables, comments added in the introduction and in the section 3, to be published in Phys. Rev.

SU(6) [70,1−][{\bf 70},1^-] baryon multiplet in the 1/Nc1/N_c expansion

The masses of excited states of mixed orbital symmetry of nonstrange and strange baryons belonging to the lowest $[{\bf 70},1^-]$ multiplet are calculated in the $1/N_c$ expansion to order $1/N_c$ with a new method which allows to considerably reduce the number of linearly independent operators entering the mass formula. This study represents an extension to SU(6) of our work on nonstrange baryons, the framework of which was SU(4). The conclusion regarding the role of the flavor operator, neglected in previous SU(6) studies, is reinforced. Namely, both the flavor and spin operators contribute dominantly to the flavor-spin breaking.Comment: 26 pages, 11 tables, to be published in PR

Baryon resonances in large NcN_c QCD

The baryon spectra are discussed in the context of the $1/N_c$ expansion approach, with emphasis on mixed symmetric states. The contributions of the spin dependent terms as a function of the excitation energy are shown explicitly. At large energies these contributions are expected to vanish.Comment: 6 pages, based on a talk given by Fl. Stancu at the Miniworkshop "Progress in Quark Models" Bled, Slovenia, July 10-17, 2006, to be published in Bled Workshops in Physics, vol. 7 no.

New look at the [70,1−][{\bf 70},1^-] baryon multiplet in the 1/Nc1/N_c expansion

So far, the masses of excited states of mixed orbital symmetry and in particular those of nonstrange $[{\bf 70},1^-]$ baryons derived in the $1/N_c$ expansion were based on the separation of a system of $N_c$ quarks into a symmetric core and an excited quark. Here we avoid this separation and show that an advantage of this new approach is to substantially reduce the number of linearly independent operators entering the mass formula. A novelty is that the isospin-isospin term becomes as dominant in $\Delta$ as the spin-spin term in $N$ resonances.Comment: 12 pages, 7 tables, to be published in Nuclear Physics

Highly Excited Baryons in Large NcN_c QCD

We use the $1/N_c$ expansion of QCD to analyse the spectrum of positive parity resonances with strangeness $S = 0, -1, -2$ and -3 in the 2--3 GeV mass region, supposed to belong to the $[\textbf{56},4^+]$ multiplet. The mass operator is similar to that of $[\textbf{56},2^+]$, previously studied in the literature. The analysis of the latter is revisited. In the $[\textbf{56},4^+]$ multiplet we find that the spin-spin term brings the dominant contribution and that the spin-orbit term is entirely negligible in the hyperfine interaction, in agreement with constituent quark model results. More data are strongly desirable, especially in the strange sector in order to fully exploit the power of this approach. We discuss possibilities of extending the calculations to other excited baryons belonging to the N=2 or the N=4 band.Comment: 10 pages, Prepared for the Workshop "Three Days of Hadronics Physics", Joint Meeting Heidelberg-Liege-Paris-Rostock, December 16-18, 2004, Spa, Belgium, to be published in AIP Proceedings. One reference adde

Negative parity baryons in the 1/Nc1/N_c expansion: the quark excitation versus the meson-nucleon resonance picture

In order to better understand the fundamental issue regarding the compatibility between the quark-shell picture and that of resonances in meson-nucleon scattering in large $N_c$ QCD we extend the work of Cohen and Lebed on mixed symmetric $\ell$ = 1 baryons to analyze excited states with $\ell$ = 3. We give an explicit proof on the degeneracy of mass eigenvalues of a simple Hamiltonian including operators up to order $\mathcal{O}(N^0_c)$ \emph{i. e.} neglecting $1/N_c$ corrections in the quark-shell picture in the large $N_c$ limit. We obtain three degenerate multiplets formed of $\ell = 3$ states, as in the case of $\ell$ = 1 baryons. The compatibility between this picture and that of resonances in meson-nucleon scattering is discussed in the light of the present results.Comment: 18 pages, 4 tables. Published version. Note that Eqs. A1, A3 and A4 contain SO(3) Clebsch-Gordan coefficients, not Wigner 3j coefficient

Matrix Elements of SU(6) Generators for Baryons at Arbitrary NcN_c

We present explicit formulas for the matrix elements of the SU(6) generators for totally symmetric spin-flavor states, relevant for baryon spectroscopy in large $N_c$ QCD. We rely on the interplay between two different methods to calculate these matrix elements. As an outcome, general analytic formulas of the corresponding SU(6) isoscalar factors are derived for arbitrary $N_c$. These results can be used to study excited states of nonstrange and strange baryons.Comment: 20 pages, 1 table, RevTeX4, version accepted for publication in Phys. Rev.

Mixed symmetric baryon multiplets in large NcN_c QCD: two and three flavours

We propose a new method to study mixed symmetric multiplets of baryons in the context of the $1/N_c$ expansion approach. The simplicity of the method allows to better understand the role of various operators acting on spin and flavour degrees of freedom. The method is tested on two and three flavours. It is shown that the spin and flavour operators proportional to the quadratic invariants of SU$_S$(2) and SU$_F$(3) respectively are dominant in the mass formula.Comment: 7 pages, 2 tables, talk given by Fl. Stancu at Mini-Workshop "Dressing Hadrons", Bled, Slovenia, July 4-11, 201